Consider \(N\)  robotic agents, indexed by the set \(\mathcal {N} \lbrace 1,\dots ,N\rbrace \) , rigidly grasping an object.
We denote by \(q_i,\dot{q}_i \in \mathbb {R}^{n_i}\) , with \(n_i\in \mathbb {N}, \forall i\in \mathcal {N}\) , the generalized joint-space variables and their time derivatives of agent \(i\) .
The overall joint configuration is then \(q [q^\top _1,\dots ,q^\top _N]^\top , \dot{q} [\dot{q}^\top _1,\dots ,\dot{q}^\top _N]^\top \in \mathbb {R}^{n}\) , with \(n \sum _{i\in \mathcal {N}}n_i\) . In addition, we denote the inertial position and rotation matrix of the \(i\) th end-effector by \(p_i\in \mathbb {R}^3\)  and \(R_i \in \mathsf {SO}(3)\) , respectively. Similarly, the velocity of the \(i\) th end-effector is denoted by \(v_i [\dot{p}_i^\top , \omega ^\top _i]^\top \) , where \(\omega _i\in \mathbb {R}^3\)  is the respective angular velocity, and it holds that \(v_i = J_i(q_i) \dot{q}_i\) , where \(J_i:\mathbb {S}_i \rightarrow \mathbb {R}^{6\times n_i}\)  is the robot Jacobian, and \(\mathbb {S}_i \lbrace q_i\in \mathbb {R}^{n_i} : \dim (\textup {null}(J_i(q_i))) = 0\rbrace \)  is the set away from kinematic singularities [1]}, \(\forall i\in \mathcal {N}\) . Moreover we denote \(x_i (p_i,R_i)\in \mathsf {SE}(3)\)  and \(x (x_1,\dots ,x_N) \in \mathsf {SE}(3)^N\) .
The task-space dynamics of the agents are [1]}:
\({M}({x})\dot{v}+{C}({x},\dot{{x}})v + {g}({x}) &= {u}-h,\) 
